I think it is fair to say that this topic is only discussed because our industry continues to use arithmetic returns in some of its models, simulations and projections. If we only spoke about returns appropriate for multi-periods calculations - ie geometric returns - then we would not have to reconcile between the two.

A related topic is the interaction between the returns generated by a portfolio and the cash inflows and outflows experienced by the portfolio. Professor Michael Drew and others have written extensively about this topic in the context of retirement incomes (e.g. Sequencing risk). More volatile portfolio returns can increase the risk of running out of money before a given point in time.